The goal of this research is to find a solution for controlling influenza evolution and its transmission. In the present paper, a new time-dependent nonlinear susceptible–infected–recovered–cross-immune model is introduced with arbitrary order Atangana–Baleanu derivative, and its solution is found using the reliable hybrid computational technique known as homotopy perturbation method via Laplace transform. The arbitrary order derivative is taken in the Liouville–Caputo sense. The outcomes of different parameters on various populations with time are displayed through graphical results. The existence and uniqueness of the solution of the presented model is discussed using Picard–Lindelof approach. Convergence analysis is also shown. The negligible error in the succeeding iterates shows the accuracy of the homotopy perturbation transform method (HPTM) scheme. The plots and the obtained results show activeness, effectiveness and suitability of HPTM scheme in solving this fractional model.